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The smallest 3-digit number which is exactly divisible by 6, 8 and 12 is ____.

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Detailed Solution

The smallest 3-digit number which is exactly divisible by 6, 8 and 12 is 120.
Here, we have to find the smallest 3-digit number which is exactly divisible by 6, 8 and 12.
Prime factorization of 6, 8, 12 is given by,
Question Image

Question Image

LCM = 2 × 2 × 2 × 3 = 24.
The multiples of 24 are,
24 × 1 = 24
24 × 2 = 48
24 × 3 = 72
24 × 4 = 96
24 × 5 = 120
24 × 6 = 144
The multiples of 24 are 24,48,72,96,120,144…...
Here 120 is the smallest 3-digit multiple of 24.
Therefore, the smallest three-digit number that is exactly divisible by 6, 8 and 120 is 120.

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